Let E,F be two Polish spaces and [X_n,Y_n],[X,Y] random variables with values in E×F (not necessarily defined on the same probability space). We show some conditions which are sufficient in order to assure that, for each bounded continuous function f on E×F, the conditional expectation of f(X_n,Y_n) given Y_n converges in distribution to the conditional expectation of f(X,Y) given Y.
Convergence results for conditional expectations
Crimaldi I;
2005-01-01
Abstract
Let E,F be two Polish spaces and [X_n,Y_n],[X,Y] random variables with values in E×F (not necessarily defined on the same probability space). We show some conditions which are sufficient in order to assure that, for each bounded continuous function f on E×F, the conditional expectation of f(X_n,Y_n) given Y_n converges in distribution to the conditional expectation of f(X,Y) given Y.File in questo prodotto:
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